I know that older bushes yield less tea than younger ones (this has been a bit of a concern in India, where many of the tea bushes are quite old and have started having reduced yields.), but what about the tea's flavor? Is it affected by the age of the bush the leaves were plucked from?

The older the tree, the deeper and further out the roots spread.With great age the roots spread into the substrata beneath the topsoil.

The older trees are thus able to extract more mineral content from the local 'rock'. This helps to provide a geographical footprint to the elements drawn from the leaves during the brewing/infusion. From areas which are famous for high quality teas the typical footprint will not be noticeable in newly planted trees which are still extracting all their goodness from (possibly fertilized) top layers of topsoil.

Wuyi Yan Cha is often produced from trees growing out of the side of cliffs, with almost zero topsoil. When these are old enough to get a good purchase in the cliff and produce enough leaf to be worth plucking - some people believe they can taste the rock in the tea.

Imen at Teahabitat espouses the use of Chao Zhou clay pots (rather than Yixing) with Chao Zhou Dan Congs - because they are made from the same clay that the older trees are extending their roots into.

An older plant is likely to have more character than a similar younger one but it really comes down to personal tastes. Someone's ideal cuppa may be leaves from a 1000 year old pu-erh tree that have been left to mature for 100 years before brewing and someone else may want the fresh leaves of a new cultivar, heavily fertilized Japanese green tea plant steamed, vaccum sealed and airmailed asap.